I have ridden enough with and without mudguards to know they make a big difference:
1. For the front, it sprays back and up. Your feet and drivetrain cops it. It is almost impossible to avoid this one though, even with mudguards. But at least you won't get sodden with dirty (and I mean DIRTY) water on your chest area.
2. For the front, it also sprays forwards and up, and because of forwards motion, you ride right into it ending up with liberal amounts on your face. What with dog excrement etc etc on the roads, I definitely don't want any of that on my face.
3. For the back, you get the wet bum and if you use a leather saddle, a wet saddle which is fatal to the saddle if ridden like that.
The wheel size is irrelevant, I have found. But the wider tyres typically used on folding bikes pick up a lot more water, so there is actually more water being sprayed. For the occasional short wet ride without mudguards, OK. But for extended riding times in rain, forget it.